mathematical modeling of biological events and cell-cell communication
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Mathematical modeling of biological events and cell-cell communication. Steve Benoit Department of Mathematics Colorado State University. - PowerPoint PPT PresentationTRANSCRIPT
STEVE BENOIT
DEPARTMENT OF MATHEMATICSCOLORADO STATE UNIVERSITY
Mathematical modeling of biological events and cell-cell
communication
This program is based upon collaborative work supported by a National Science Foundation Grant No. 0841259; Colorado State University, Thomas Chen, Principal Investigator, Michael A. de Miranda and Stuart Tobet Co-Principal Investigators. Any opinions, findings, conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Mathematical Models in Biology
MODEL
DATA
EXPERIMENT
BIOLOGICAL SYSTEM
The Biological System
History: “Top-Down” Models
Continuum model of cell concentration(Keller, Segel -1971)
History: “Top-Down” Models
Continuum model of cell concentration (Keller & Segel -1971)
Random walk with bias (Alt – 1980)
History: “Top-Down” Models
Continuum model of cell concentration (Keller & Segel -1971)
Random walk with bias (Alt – 1980)
Stochastic model(Tranquillo – 1988)
History: “Top-Down” Models
Continuum model of cell concentration (Keller & Segel -1971)
Random walk with bias (Alt – 1980)
Stochastic model(Tranquillo – 1988)
Hyperbolic continuum model(Hillen & Stevens - 2000)
History: “Bottom-Up” Models
Molecular dymanics models
History: “Bottom-Up” Models
Molecular dymanics models
Membrane models
History: “Bottom-Up” Models
Molecular dymanics models
Membrane models
Cytoskeleton models
History: “Bottom-Up” Models
Molecular dymanics models
Membrane models
Cytoskeleton models
Adhesion modulation models
The Challenge…
No model can capture the complexity of the biological system
The Challenge…
The goal is to capture critical behaviors while ignoring the rest:
“Make everything as simple as possible but no simpler.”
- A. Einstein
How do we know what to ignore? Experiment and data…
Data Gathering Process
Extract individual frames from videosCompensate for global motion
Data Gathering Process
Extract individual frames from videosCompensate for global motionIdentify cells by finding local maxima
Data Gathering Process
Extract individual frames from videosCompensate for global motionIdentify cells by finding local maximaCorrelate cell positions between frames
Data Gathering Process
Extract individual frames from videosCompensate for global motionIdentify cells by finding local maximaCorrelate cell positions between framesConstruct trajectories
Data Gathering Process
Trajectories overlaid on motion-compensated video:
Data Gathering Process
Extract individual frames from videosCompensate for global motionIdentify cells by finding local maximaCorrelate cell positions between framesConstruct trajectoriesCategorize by region within the domain
Motion Analysis
Add coordinate system based on tissue orientation
Motion Analysis
Add coordinate system based on tissue orientation
Trajectory start, end frames, distance, avg. speed
Motion Analysis
Add coordinate system based on tissue orientation
Trajectory start, end frames, distance, avg. speed
Avg. direction (angle), diffusion model parameters
2( ) 4r r Kt
Motion Analysis
Add coordinate system based on tissue orientation
Trajectory start, end frames, distance, avg. speed
Avg. direction (angle), diffusion model parameters
Analysis groups:By region By length of trajectory (long vs. short)By average speed (slow vs. fast)By age (start frame)
2( ) 4r r Kt
Analysis Results
Distribution of direction of motion:
Region 1
Region 2
Region 3
Region 4
Whole population:
Distance > 15:
Avg. speed > 0.9:
Analysis Results
Correlation of direction with speed and distance:Region
1
Region 2
Region 3
Region 4
0 10 20 30 40 50 60 70 80 90 100-180
-120
-60
0
60
120
180
R² = 0.200917212811551
0 20 40 60 80 100 120 140 160-180
-120
-60
0
60
120
180
R² = 0.0625699568105396
0 10 20 30 40 50 60 70 80 90-180
-120
-60
0
60
120
180
R² = 0.0253260962805287
0 10 20 30 40 50 60 70 80-180
-120
-60
0
60
120
180
R² = 0.273293087579952
Analysis Results
Correlation of speed with cell age (start frame):Region
1
Region 2
Region 3
Region 4
0 5 10 15 20 25 300.0
0.5
1.0
1.5
2.0
2.5
3.0
R² = 0.0255178189614795
0 5 10 15 20 25 300.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
R² = 0.0981739728660867
0 5 10 15 20 25 30 350.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
R² = 0.00391820513749996
0 5 10 15 20 25 300.00.20.40.60.81.01.21.41.61.8
R² = 0.12445147974987
Interpretation
Strong correlation of motion direction with region in regions 1 and 4, weaker in 2, and weaker still in 3.
Long and fast motions exhibit a preferred direction, which is most pronounced in regions 1 and 4.
Conclusion: Cell motion is being directed by a signaling mechanism in regions 1 and 4
Model Components
MembraneCytoskeleton / Chemotaxis
Interactions
Questions?
Acknowledgements
Colorado State UniversityTom ChenStuart TobetThe Tobet LabMatt StrattonKrystle FrahmCheryl Hartshorn
University of LjubljanaGregor MajdičDrago Strle
Jožef Stefan InstitutePrimož Ziherl